Sarah Jane Hamilton

Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D

Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included.

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D

A direct reconstruction algorithm for complex conductivities in W2,∞ (Ω), where Ω is a bounded, simply connected Lipschitz domain in ℝ2, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Survival and Breeding Transitions for a Reintroduced Bison Population: a Multistate Approach

Abstract The iconic plains bison (Bison bison) have been reintroduced to many places in their former range, but there are few scientific data evaluating the success of these reintroductions or guiding the continued management of these populations. Relying on mark–recapture data, we used a multistate model to estimate bison survival and breeding transition probabilities while controlling for the recapture process. We tested hypotheses in these demographic parameters associated with age, sex, reproductive state, and environmental variables. We also estimated biological process variation in survival and breeding transition probabilities by factoring out sampling variation. The recapture rate of females and calves was high (0.78 ± 0.15 [SE]) and much lower for males (0.41 ± 0.23), especially older males (0.17 ± 0.15). We found that overall bison survival was high (>0.8) and that males (0.80 ± 0.13) survived at lower rates than females (0.94 ± 0.04), but as females aged survival declined (0.89 ± 0.05 for F ≥15 yr old). Lactating and non-lactating females survived at similar rates. We found that females can conceive early (approx. 1.5 yr of age) and had a high probability (approx. 0.8) of breeding in consecutive years, until age 13.5 years, when females that were non-lactating tended to stay in that state. Our results suggest senescence in reproduction and survival for females. We found little support for the effect of climatic covariates on demographic rates, perhaps because the parks current population management goals were predicated from drought-year conditions. This reintroduction has been successful, but continued culling actions will need to be employed and an adaptive management approach is warranted. Our demographic approach can be applied to other heavily managed large-ungulate systems with few or no natural predators.

A direct reconstruction method for anisotropic electrical impedance tomography

A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the isothermal coordinates on the boundary of the domain. Non-uniqueness of the inverse problem is dealt with by recovering the unique isotropic conductivity that can be achieved as a deformation of the measured anisotropic conductivity by isothermal coordinates. The method shows how isotropic D-bar reconstruction methods have produced reasonable and informative reconstructions even when used on EIT data known to come from anisotropic media, and when the boundary shape is not known precisely. Furthermore, the results pave the way for regularized anisotropic EIT. Key aspects of the approach involve D-bar methods and inverse scattering theory, complex geometrical optics solutions and quasi-conformal mapping techniques.

A DATA-DRIVEN EDGE-PRESERVING D-BAR METHOD FOR ELECTRICAL IMPEDANCE TOMOGRAPHY

In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface. The reconstruction task is a highly ill-posed nonlinear inverse problem, which is very sensitive to noise, and requires the use of regularized solution methods, of which D-bar is the only proven method. The resulting EIT images have low spatial resolution due to smoothing caused by low-pass filtered regularization. In many applications, such as medical imaging, it is known a priori that the target contains sharp features such as organ boundaries, as well as approximate ranges for realistic conductivity values. In this paper, we use this information in a new edge-preserving EIT algorithm, based on the original D-bar method coupled with a deblurring flow stopped at a minimal data discrepancy. The method makes heavy use of a novel data fidelity term based on the so-called CGO sinogram. This nonlinear data step provides superior robustness over traditional EIT data formats such as current-to-voltage matrices or Dirichlet-to-Neumann operators, for commonly used current patterns.

EIT Imaging of admittivities with a D-bar method and spatial prior: experimental results for absolute and difference imaging

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a bodys surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a noise-robust regularized image reconstruction method. In this work, the a priori D-bar method for complex admittivities is demonstrated effective on experimental tank data for absolute imaging for the first time. Additionally, the method is adjusted for, and tested on, time-difference imaging scenarios. The ability of the method to be used for conductivity, permittivity, absolute as well as time-difference imaging provides the user with great flexibility without a high computational cost.

A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography

The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar method produces reconstructions with sharper edges and improved contrast. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain, thereby increasing the radius of the low-pass filter. The algorithm is tested on numerically simulated noisy EIT data and d...

Robust computation in 2D absolute EIT (a-EIT) using D-bar methods with the ‘exp’ approximation

OBJECTIVE Absolute images have important applications in medical electrical impedance tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors. APPROACH The effects of errors in domain shape and electrode placement on absolute images computed with 2D D-bar reconstruction algorithms are studied on experimental data. MAIN RESULTS It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from such modeling errors are similar to those occurring in classic time-difference EIT imaging. SIGNIFICANCE This study is promising for clinical applications where absolute EIT images are desirable but previously thought impossible.